Abstract We study standing-wave solutions of Born–Infeld electrodynamics, with nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the electromagnetic field has only one nonzero component depending on time and on the coordinate perpendicular to the plates. The problem then reduces to solving the scalar Born–Infeld equation, a nonlinear partial differential equation in 1+1 dimensions. We apply two alternative methods to obtain standing-wave solutions to the Born–Infeld equation: an iterative method, and a “minimal surface” method. We also study standing wave solutions in a uniform constant magnetic field background. The results obtained in this work provide a theoretical background for experimental tests of Born–Infeld theory.

中文翻译：

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Born-Infeld 理论中的驻波解

摘要 我们研究了波恩-因菲尔德电动力学的驻波解，在两个平行导电板之间的区域中具有非零电磁场。我们考虑最简单的情况，当描述电磁场的矢量势只有一个取决于时间和垂直于板的坐标的非零分量时发生。然后问题简化为求解标量 Born-Infeld 方程，这是一个 1+1 维的非线性偏微分方程。我们应用两种替代方法来获得 Born-Infeld 方程的驻波解：迭代方法和“最小表面”方法。我们还研究了均匀恒定磁场背景下的驻波解。在这项工作中获得的结果为 Born-Infeld 理论的实验测试提供了理论背景。